What is the Greatest Common Factor of 10485 and 10500?

Greatest common factor (GCF) of 10485 and 10500 is 15.

GCF(10485,10500) = 15

We will now calculate the prime factors of 10485 and 10500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10485 and 10500.

How to find the GCF of 10485 and 10500?

We will first find the prime factorization of 10485 and 10500. After we will calculate the factors of 10485 and 10500 and find the biggest common factor number .

Step-1: Prime Factorization of 10485

Prime factors of 10485 are 3, 5, 233. Prime factorization of 10485 in exponential form is:

10485 = 3² × 5¹ × 233¹

Step-2: Prime Factorization of 10500

Prime factors of 10500 are 2, 3, 5, 7. Prime factorization of 10500 in exponential form is:

10500 = 2² × 3¹ × 5³ × 7¹

Step-3: Factors of 10485

List of positive integer factors of 10485 that divides 10485 without a remainder.

1, 3, 5, 9, 15, 45, 233, 699, 1165, 2097, 3495

Step-4: Factors of 10500

List of positive integer factors of 10500 that divides 10485 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 125, 140, 150, 175, 210, 250, 300, 350, 375, 420, 500, 525, 700, 750, 875, 1050, 1500, 1750, 2100, 2625, 3500, 5250

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10485 and 10500. The biggest common factor number is the GCF number.
So the greatest common factor 10485 and 10500 is 15.

Also check out the Least Common Multiple of 10485 and 10500